On 17 October 2018, BBC Radio 3 will broadcast a 15 minute programme at 10.45 pm (BST) on Tolkien’s Forest of Mirkwood.
From the Radio Times: “Eleanor Rosamund Barraclough is joined by Mark Atherton from Oxford university for a walk through J.R.R. Tolkien’s forest, uncovering the influence of the woodiest of Norse sagas on the creation of Middle-earth.”

It is likely to be available after broadcast for over a year here: https://www.bbc.co.uk/programmes/m0000qj9
from the BBC iPlayer website: There’s a shadow creeping across the forest in the works of J.R.R. Tolkien. Nature may be incorruptible but the creatures of the forest cannot withstand the relentless march of evil. Slowly but surely the songbirds are replaced by giant spiders, black squirrels and rampaging goblins…
The first programme was about forests in the work of William Morris, which also name-checked Tolkien: https://www.bbc.co.uk/programmes/m0000r1s
Other programmes deal with the Brothers Grimm, The Jungle Book and A.A. Milne.